The purpose of this project is to improve the remission induction rate of acute lymphocytic leukemia in adult patients utilizing vincristine and dexamethasone with intermittent moderate doses of methotrexate followed by asparaginase. A second objective is to decrease the incidence of severe infections during induction therapy by utilizing oral non-absorbable antibiotics. A third objective is to determine whether intermittent high dose methotrexate with leucovorin rescue and with vincristine and dexamethasone will prolong remission duration. The fourth objective is to determine the efficacy of moderate and high dose methotrexate in preventing meningeal leukemia and to correlate the clinical effectiveness with the cerebrospinal fluid methotrexate levels. To date 33 patients have been entered onto this study. Eighteen patients had no prior treatment, fifteen had prior treatment. Of the no-prior-treatment patients, five patients are still on study and 13 are off study. Complete remissions have been achieved in 14 of the 18 (78%) patients that went through induction. Of the prior treatment patients, ten of thirteen (77%) achieved complete remission. The median survival for complete remission patients for both groups is 16-plus months and for all treated patients for both groups is 10-plus months.